Abstract:
The new sufficient conditions of a conditional stability of the trivial solution of a system of the ordinary quadratic differential equations are obtained. For the homogeneous system a domains of unlocal stability are also indicated (it will be cones). Then this domain is used for design of piecewise linear (discontinuous) control lawes on output for a bilinear control system of any order. Thus a system closed by such discontinuous feed-back becomes globally stable in the Lyapunuv sense for all the state space. The examples are given.
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